Question

which rule explains why these triangles are congruent?
options: sss, asa, aas, sas, these triangles cannot be proven congruent.

Explanation:

Step1: Identify shared side

The two triangles $\triangle XYW$ and $\triangle YVX$ share the side $XV$ (or $XV$ is common to both $\triangle XWV$ and $\triangle VYX$).

Step2: Match marked angles

We have $\angle WXV = \angle YVX$ (double red arcs) and $\angle XWV = \angle VXY$ (single red arcs), with the shared side $XV$ lying between these two pairs of angles.

Step3: Match congruence rule

This matches the ASA (Angle-Side-Angle) rule, where two angles and the included side of one triangle are equal to the corresponding two angles and included side of the other triangle.

Answer:

ASA